Iterative Algorithms for Crystal Efficiency Estimation in PET
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Solution Overview
Problem
Current methods for estimating crystal efficiency in PET systems are not directly applicable to time-of-flight (TOF) compressed normalization data, complicating the normalization data model equations and requiring new approaches for accurate estimation.
Innovation Solution
The development of simple update iterative algorithms, including a monotonic sequential coordinate descent algorithm and a simultaneous update algorithm, which optimize the Least Squares objective function to estimate crystal efficiencies from TOF compressed normalization data, allowing easy adaptation to any acquisition geometry and parallelization.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If TOF compressed normalization data is used, then data storage requirements are reduced and processing efficiency is improved, but the normalization data model equations become complicated and existing crystal efficiency estimation methods are no longer directly applicable
Solution Approach 1:
The patent transforms the complex TOF compressed normalization data model into a simplified form by changing the parameter representation. It introduces new parameters (crystal efficiency components and geometric factors) that separate the physical properties from the compression effects, allowing the model to be solved using iterative algorithms similar to those used for uncompressed data.
Solution Approach 2:
The patent replaces the direct mathematical inversion approach with an iterative optimization algorithm. Instead of solving the complicated normalized equations directly, it uses an iterative method that gradually converges to the crystal efficiency values, substituting a computational approach that is more manageable despite the model complexity.
2Ease of manufacture
If traditional crystal efficiency estimation methods are used on TOF compressed data, then processing is simpler, but accurate estimation cannot be achieved due to model complications
Solution Approach 1:
The patent segments the normalization data model into distinct components: crystal efficiency factors, geometric factors, and compression factors. By separating these elements, the patent enables the use of iterative algorithms that can estimate crystal efficiencies accurately while accounting for the TOF compression effects, thus maintaining both processing feasibility and estimation accuracy.
Solution Approach 2:
The patent introduces intermediate variables representing crystal efficiency components that serve as mediators between the raw TOF compressed data and the final efficiency estimates. These intermediaries allow the complex relationship to be broken down into manageable iterative updates, achieving both accuracy and computational tractability.
3Measurement precision
If iterative algorithms are developed for TOF compressed data, then accurate crystal efficiency estimation is achieved, but algorithm complexity and computational resources increase
Solution Approach 1:
The patent employs dynamic iterative algorithms that adaptively update crystal efficiency estimates based on the TOF compressed normalization data. The algorithms dynamically adjust the efficiency values through multiple iterations, allowing accurate estimation while managing computational complexity through efficient update rules and convergence criteria.
4Quantity of substance
If TOF compression is applied, then data storage is reduced, but the rebinning process becomes more complex
Solution Approach 1:
The patent performs preliminary decomposition of the TOF compressed data into crystal efficiency components and geometric factors before the main estimation process. This preliminary action simplifies the subsequent rebinning process by pre-organizing the data in a format that preserves natural LOR sampling while reducing storage requirements, thus managing the complexity of the rebinning operation.
Data Source
AI summary
Time-of-flight (TOF) clinical data collected during a PET scan are very sparse and have significant size. These data undergo TOF axial rebinning and azimuthal mashing if histogrammed data-based reconstruction algorithms are used. In a clinical environment, TOF compression is typically performed by the hardware rebinner. Normalization data, acquired on a regular basis and used for estimation of some norm components, are compressed by the hardware rebinner in a similar manner. This disclosure presents simple update iterative algorithms for crystal efficiencies norm component estimation from TOF compressed normalization data. Previously known methods are not directly applicable since the compression procedure significantly complicates normalization data model equations. The iterative algorithms presented herein have advantages of being easily adapted to any acquisition geometry, and of allowing estimation of parameters at crystal level when a number of crystals is relatively small. A monotonic sequential coordinate descent algorithm, which optimizes the Least Squares objective function, is presented. A simultaneous update algorithm, which possesses the advantage of easy parallelization, is also presented.